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At least 55 records · Page 3

Making statistical inferences about software reliability

Failure times of software undergoing random debugging can be modelled as order statistics of independent but nonidentically distributed exponential random variables. Using this model inferences can be made about current reliability and, if debugging continues, future reliability. This model also shows the difficulty inherent in statistical verification of very highly reliable software such as that used by digital avionics in commercial aircraft.

Miller, Douglas R.↗

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

Newman, Perry A.↗

Subband Image Coding with Jointly Optimized Quantizers

An iterative design algorithm for the joint design of complexity- and entropy-constrained subband quantizers and associated entropy coders is proposed. Unlike conventional subband design algorithms, the proposed algorithm does not require the use of various bit allocation algorithms. Multistage residual quantizers are employed here because they provide greater control of the complexity-performance tradeoffs, and also because they allow efficient and effective high-order statistical modeling. The resulting subband coder exploits statistical dependencies within subbands, across subbands, and across stages, mainly through complexity-constrained high-order entropy coding. Experimental results demonstrate that the complexity-rate-distortion performance of the new subband coder is exceptional.

Kossentini, Faouzi↗

Representativeness of CO and O3 Along ATom Transects Derived from GEOS-5 and GMI-CTM Simulations

One major goal for the NASA Atmospheric Tomography Mission (ATom) is producing an observation-based chemical climatology to represent the atmospheric heterogeneity. In this study, we use CO and O3 observations and global atmospheric model simulations to examine the spatial representativeness of the ATom-1 and -2 transects within a 4D framework provided by the NASA GEOS-5 and GMI-CTM models. Based on the probability density functions, we find that the variability of CO and O3 along the flight tracks is well hindcast by the model when sampled per ATom flights. The CO variations along the ATom-transect are likely representative of the typical CO variations over the whole Pacific basin during both the ATom-1 and -2 periods, the northern Atlantic during the ATom-1 period, and the tropical Atlantic in the ATom-2 period. Over southern Atlantic, CO along the ATom-1 transects is likely less well mixed than that of the broader region, but is still representative of the median CO concentration. CO along the ATom-2 transect is likely higher than the median CO concentration over this region. For O3, the agreements between PDFs of O3 sampled along the ATom transects and over the broader regions are fair to good over all six regions (Scores > 0.65) with notable discrepancies over some regions. For example, in ATom-1 over the northern Pacific and Atlantic, the transect samples air masses with higher O3 levels. During ATom-2, the transect over-represents the occurrence of O3 plumes over tropical Pacific. Over the southern Pacific and Atlantic for both ATom-1 and -2, the transects have a less uniform distribution compared to the surrounding basins, but still represent the median O3 abundance. Overall, we conclude in most cases that ATom measurements represent the statistical variations of these two species over the ocean basins at the time of measurement. Higher-order statistics, including covariance of species, has not been tested in this study.

ozone↗

Detector noise statistics in the non-linear regime

The statistical behavior of an idealized linear detector in the presence of threshold and saturation levels is examined. It is assumed that the noise is governed by the statistical fluctuations in the number of photons emitted by the source during an exposure. Since physical detectors cannot have infinite dynamic range, our model illustrates that all devices have non-linear regimes, particularly at high count rates. The primary effect is a decrease in the statistical variance about the mean signal due to a portion of the expected noise distribution being removed via clipping. Higher order statistical moments are also examined, in particular, skewness and kurtosis. In principle, the expected distortion in the detector noise characteristics can be calibrated using flatfield observations with count rates matched to the observations. For this purpose, some basic statistical methods that utilize Fourier analysis techniques are described.

Shopbell, P. L.↗

Directional spectra of ocean waves from microwave backscatter: A physical optics solution with application to the short-pulse and two-frequency measurement techniques

Two simple microwave radar techniques that are potentially capable of providing routine satellite measurements of the directional spectrum of ocean waves were developed. One technique, the short pulse technique, makes use of very short pulses to resolve ocean surface wave contrast features in the range direction; the other technique, the two frequency correlation technique makes use of coherency in the transmitted waveform to detect the large ocean wave contrast modulation as a beat or mixing frequency in the power backscattered at two closely separated microwave frequencies. A frequency domain analysis of the short pulse and two frequency systems shows that the two measurement systems are essentially duals; they each operate on the generalized (three frequency) fourth-order statistical moment of the surface transfer function in different, but symmetrical ways, and they both measure the same directional contrast modulation spectrum. A three dimensional physical optics solution for the fourth-order moment was obtained for backscatter in the near vertical, specular regime, assuming Gaussian surface statistics.

Jackson, F. C.↗

Texture classification by local rank correlation

A new approach to texture classification based on local rank correlation is proposed here. Its performance is compared with Laws' method which uses local convolution with feature masks. In the experiments, texture samples are classified based on their distribution of local statistics, either rank correlations or convolutions. The new method achieves generally optimal classification rates. It appears to be more robust because local order statistics are unaffected by local sample differences due to monotonic shifts of texture gray values and are less sensitive to noise.

Harwood, D.↗

Quantile Vocoder

Parameters of spectral envelope obtained statistically. Algorithm for digital compression of speech signals encodes power spectral density of each short interval of speech by use of quantiles or order statistics. Purpose to reduce bit rate and bandwidth required for transmission. When fully developed, quantile vocoder - speech-encoding system based on new algorithm - expected moderately complicated compared with other speech-encoding systems and reproduce high-quality speech from code transmitted at relatively low bit rates. Speech signal treated mathematically as though amplitude spectrum stationary during short coding intervals, called "windows". Window duration of 20 or 35 ms, chosen as compromise between frequency resolution and time resolution. During each window, short-time amplitude and power spectra found by sampling at high rate (typically 10 kHz) and taking fast Fourier transforms (FFT's).

Swaminathan, Kumar↗

A statistical model of the photomultiplier gain process with applications to optical pulse detection

A Markov diffusion model was used to determine an approximate probability density for the random gain. This approximate density preserves the correct second-order statistics and appears to be in reasonably good agreement with experimental data. The receiver operating curve for a pulse counter detector of PMT cathode emission events was analyzed using this density. The error performance of a simple binary direct detection optical communication system was also derived.

Tan, H. H.↗

A statistical model of the photomultiplier gain process with applications to optical pulse detection

A Markov diffusion model was used to determine an approximate probability density for the random gain. This approximate density preserves the correct second-order statistics and appears to be in reasonably good agreement with experimental data. The receiver operating curve for a pulse counter detector of PMT cathode emission events was analyzed using this density. The error performance of a simple binary direct detection optical communication system was also derived. Previously announced in STAR as N82-25100

Tan, H. H.↗

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

Ristorcelli, J. R.↗

Statistics for ionospherically diffracted VHF/UHF signals.

In this paper, a general characterization of the statistics for an ionospherically diffracted, monochromatic plane wave is presented. The main results are restricted to weak scatter, although two possible extensions that accommodate large phase perturbations and multiple scatter are discussed. A detailed discussion of the first-order statistics of amplitude is given. The general Gaussian distribution is discussed together with its Nakagami-distribution approximation and the log-normal distribution. By using a segment of ATS-3 satellite data recorded at Lima, Peru, we show equally good fits to Gaussian and log-normal distributions at least for the limited dynamic range available. The Nakagami distribution provides only a poor approximation.

Rino, C. L.↗

High Order Entropy-Constrained Residual VQ for Lossless Compression of Images

High order entropy coding is a powerful technique for exploiting high order statistical dependencies. However, the exponentially high complexity associated with such a method often discourages its use. In this paper, an entropy-constrained residual vector quantization method is proposed for lossless compression of images. The method consists of first quantizing the input image using a high order entropy-constrained residual vector quantizer and then coding the residual image using a first order entropy coder. The distortion measure used in the entropy-constrained optimization is essentially the first order entropy of the residual image. Experimental results show very competitive performance.

Kossentini, Faouzi↗

Modeling of the reactant conversion rate in a turbulent shear flow

Results are presented of direct numerical simulations (DNS) of spatially developing shear flows under the influence of infinitely fast chemical reactions of the type A + B yields Products. The simulation results are used to construct the compositional structure of the scalar field in a statistical manner. The results of this statistical analysis indicate that the use of a Beta density for the probability density function (PDF) of an appropriate Shvab-Zeldovich mixture fraction provides a very good estimate of the limiting bounds of the reactant conversion rate within the shear layer. This provides a strong justification for the implementation of this density in practical modeling of non-homogeneous turbulent reacting flows. However, the validity of the model cannot be generalized for predictions of higher order statistical quantities. A closed form analytical expression is presented for predicting the maximum rate of reactant conversion in non-homogeneous reacting turbulence.

Frankel, S. H.↗

Studies in Astronomical Time Series Analysis: VII. An Enquiry Concerning Non-Linearity, the RMS-Mean Flux Relation, and log-Normal Flux Distributions

A broad and widely used class of stationary, linear, additive time series models can have statistical properties which many authors have asserted imply that the underlying process must be non-linear, non-stationary, multiplicative, or inconsistent with shot noise. This result is demonstrated with exact and numerical evaluation of the model flux distribution function and dependence of flux standard deviation on mean flux (here and in the literature called the rms-flux relation). These models can: (1) exhibit normal, log-normal or other flux distributions; (2) show linear or slightly non-linear rms-mean flux dependencies; as well as (3) match arbitrary second order statistics of the time series data. Accordingly the above assertions cannot be made on the basis of statistical time series analysis alone. Also idscussed are ambiguities in the meaning of terms relevant to this study – linear, stationary and multiplicative – and functions that can transform observed fluxes to a normal distribution as well or better than the logarithm.

Jeffrey D Scargle↗